where \(\operatorname{expit}(\cdot )=\exp (\cdot )/[1+\exp (\cdot )]\) , \(\hat{\beta }_0\)  and \(\hat{\mathbf {\beta }}_{\mathbf {1}}\)  are point estimates of the logistic regression parameters, and \(\hat{e}_i\)  is an estimate of \(e_i\) . Inverse probability of treatment weights are constructed by taking the reciprocal of the estimated conditional probability of the treatment assigned in the index study [1]}. That would be \(1/\hat{e}_i\)  for units under treatment \(A\)  and \(1/(1-\hat{e}_i)\)  for units under treatment \(C\) .
